5.5.1. Time Complexity Overview

Try these first

1. 1.

   What is Kruskal's Algorithm used for?

   Hint

   Think about what you need to connect all nodes in a graph.

2. 2.

   Why do we sort edges in Kruskal's Algorithm?

   Hint

   Consider the cost of connections.

3. 3.

   What is the primary purpose of Kruskal's Algorithm?

   • To find all paths in a graph
   • To find the minimum spanning tree
   • To sort a graph

   Hint

   Think about what you need to do to connect all points with the least cost.

4. 4.

   True or False: Cycle detection is optional in Kruskal's Algorithm.

   • True
   • False

   Hint

   Consider what happens if cycles occur.

5. 5.

   Implement Kruskal's algorithm on a graph with 5 vertices (1 to 5) and the following edges and weights: (1,2,1), (1,3,3), (2,3,2), (2,4,4), (3,5,6). What is the minimum spanning tree?

   Hint

   Follow the steps of edge selection carefully.

6. 6.

   Analyze the impact of using an efficient union-find structure versus a basic merging approach in terms of Kruskal’s algorithm performance on a densely connected graph.

   Hint

   Consider how often you need to check for cycles.